All of the 5th grade teachers and students from Oak went on a field trip to an archaeology museum. Tickets were $$8.00$ each for teachers and $$2.50$ each for students, and the group paid $$47.00$ in total. A few weeks later, the same group visited a natural history museum where the tickets cost $$24.00$ each for teachers and $$8.50$ each for students, and the group paid $$147.00$ in total. Find the number of teachers and students on the field trips.
Explanation: Let $x$ equal the number of teachers and $y$ equal the number of students. The system of equations is: ${8x+2.5y = 47}$ ${24x+8.5y = 147}$ Solve for $x$ and $y$ using elimination. Multiply the top equation by $-3$ ${-24x-7.5y = -141}$ ${24x+8.5y = 147}$ Add the top and bottom equations together. ${y = 6}$ Now that you know ${y = 6}$ , plug it back into $ {8x+2.5y = 47}$ to find $x$ ${8x + 2.5}{(6)}{= 47}$ $8x+15 = 47$ $8x = 32$ $x = \dfrac{32}{8}$ ${x = 4}$ You can also plug ${y = 6}$ into $ {24x+8.5y = 147}$ and get the same answer for $x$ ${24x + 8.5}{(6)}{= 147}$ ${x = 4}$ There were $4$ teachers and $6$ students on the field trips.